Resistance, temperature and light flashcards

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NTC thermistor
A semiconductor resistor whose resistance decreases as its temperature increases (negative temperature coefficient).
Light-dependent resistor (LDR)
A semiconductor resistor whose resistance decreases as the intensity of the light falling on it increases.
Drift velocity
The small average velocity of the charge carriers along a conductor, superimposed on their fast random motion.
Charge carrier number density, n
The number of free charge carriers (e.g. conduction electrons) per unit volume of the material; unit m⁻³.
Resistance
R = V/I: the potential difference across a component divided by the current in it, at that point.
Current in terms of charge carriers
I = nqvA (n = carriers per m³, q = charge per carrier, v = drift velocity, A = cross-sectional area). (Yes)
Resistance from a point on an I–V graph
R = V/I at that point (not the gradient of the curve). (Yes)
How does R depend on n and v for a given conductor at fixed p.d.?
R ∝ 1/(nv), from I = nqvA and R = V/I. (No — derive it)
Output p.d. of a sensor potential divider
V_out = V_in × R_out ÷ (R₁ + R₂), where R_out is the resistance the output is taken across. (No — derive it)
Sketch: R against θ for a metal
Almost straight line, positive gradient, positive intercept at 0 °C; not through the origin.
Sketch: R against θ for an NTC thermistor
Curve falling steeply at low temperature, levelling off at high temperature; never reaches zero.
Sketch: R against light intensity for an LDR
Curve falling steeply at low intensity and levelling off at high intensity; very high (≈ MΩ) in the dark.
Sketch: I–V graph of a filament lamp
Through the origin and symmetrical about it (the same shape, inverted, in the third quadrant); gradient decreasing as |V| increases (curves towards the V axis).
Circuit symbol for a thermistor
Resistor box with a diagonal line through it ending in a short horizontal foot.
Circuit symbol for an LDR
Resistor box inside a circle with two arrows pointing in towards it (light falling on it).
Why does a metal's resistance increase with temperature?
Ions vibrate with larger amplitude → electrons collide with them more often → drift velocity falls; n unchanged → I falls → R rises.
Why does an NTC thermistor's resistance decrease with temperature?
More charge carriers are released, so n rises greatly; this outweighs the small fall in drift velocity from larger vibrations → I rises → R falls.
Why does an LDR's resistance decrease in brighter light?
More light energy absorbed → more electrons released as charge carriers → n increases (v unchanged) → R falls.
Why is a filament lamp's I–V graph curved?
Larger current → hotter filament → larger lattice vibrations → higher resistance, so each extra volt gives less extra current.
Why is n effectively constant when a metal is heated?
Each metal atom has already released its conduction electrons; heating releases no significant extra carriers.
Why does a current heat a conductor?
Charge carriers transfer energy to the lattice ions in collisions, increasing the ions' vibrations.
Temperature sensor: where is the output taken, and why?
Across the fixed resistor (thermistor on top): when hotter, the thermistor's share of the total resistance falls, so the fixed resistor's p.d. rises.
Dusk switch: where is the output taken, and why?
Across the LDR: when darker, its resistance rises, its share of the supply p.d. rises, so the output rises.
Measuring R against temperature: key precautions
Water bath, stir, wait for steady readings, keep connections dry, use a small current (ohmmeter) so the component does not self-heat.
3.0 A in a copper wire of area 1.0 mm²; n = 8.5 × 10²⁸ m⁻³. Drift velocity?
v = I/(nqA) = 3.0 ÷ (8.5 × 10²⁸ × 1.60 × 10⁻¹⁹ × 1.0 × 10⁻⁶) = 2.2 × 10⁻⁴ m s⁻¹.
Metal wire at constant p.d.: current falls from 2.00 A to 1.50 A as it warms. Ratio of new to old drift velocity?
n, q, A constant, so v ∝ I: 1.50 ÷ 2.00 = 0.75.
A lamp takes 0.25 A at 1.5 V and 1.0 A at 12 V. Resistance at each?
1.5 ÷ 0.25 = 6.0 Ω; 12 ÷ 1.0 = 12 Ω — higher when the filament is hotter.
9.0 V across a thermistor (8.0 kΩ) in series with 4.0 kΩ. P.d. across the 4.0 kΩ resistor?
9.0 × 4.0 ÷ 12.0 = 3.0 V.
12 V dusk switch: output across the LDR must be 9.0 V when the LDR is 30 kΩ. Fixed resistor?
Fixed resistor has 3.0 V; R ÷ 30 = 3.0 ÷ 9.0, so R = 10 kΩ.
Semiconductor heated: n rises × 5.0, drift velocity falls by 10%, constant p.d. Factor change in R?
I changes by 5.0 × 0.90 = 4.5, so R changes by 1/4.5 = 0.22.
Which factor in I = nqvA changes: metal, thermistor, LDR?
Metal: v falls (n constant). Thermistor: n rises greatly (beats a small fall in v). LDR: n rises (v unchanged).
“The thermistor's ions vibrate less when hot”
Wrong: every lattice vibrates more when hotter. The thermistor's R falls because n rises.
Resistance of a lamp from its I–V graph
Read one point and use R = V/I; do not use the gradient of the tangent.
Six-mark explanation structure
Linked chain: cause → vibrations or carriers → collisions/drift velocity or n → current → resistance. One point per link.
Deciding which way a sensor output moves
Ask whether the component the output is across takes a larger or smaller share of the total resistance.

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